1 real number system-1

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Concept #1 - The Real Number System & Number Line Fall, 2013

Overview: Remember the idea behind concept labs; you will

work on an assignment that explores a major mathematical

and algebraic concept. This lab consists of three parts:

1. In-class discussion and activity

2. Individual concept questions

3. Individual in-class essay

The essay will be on ______________________________________.

1. Infinity and Sets of Numbers

Watch the AT&T commercial Infinity . Take a couple minutes to think about the following questions andthen write your thoughts below. Write in complete sentences. You do not need to answer all the

questions and you may write about other ideas that the commercial may have evoked. You have 10-

minutes! After the 10 minutes, we will discuss these questions, your comments and introduce some

important vocab.

Is infinity a number?

Can we count to infinity?

How big is infinity?

Does “infinity plus infinity” make sense?

How are Real numbers classified?

Which group of numbers is bigger: whole numbers or natural numbers?




2. The Real Number System and The Number Line

We discussed how some groups – or sets – of numbers are bigger than others even though each of these

sets have infinite numbers in them. What a crazy idea! Below is a visual representation of those sets of

numbers.

Your first task is to identify two numbers that fall into each category represented in the visual above.

These numbers should be between -10 and 10. Identify these numbers by writing them in the

appropriate bubble in the visual and drawing them in the correct location on the number line.

True or False: Identify the statement as true or false. If always true, write “true.” If false, give a numeric

example that shows it is false.

EX. When you add two integers together, the result is a positive integer. _________False_________

-2 + (-4) = -6. Since -2 and -4 are both integers, but -6 is not positive, the statement is not always true.

1. Adding two rational numbers together always results in a rational number. ________________________

2. Adding a whole number to a natural number results in the same natural number. ________________________

Real Numbers




3. Multiplying two irrational numbers always results in another irrational number. ________________________

4. The number 4 is a Natural number and it is also a Whole number. ________________________

5. The number -5 can be classified as Real, Rational, Integer, and Whole. ________________________

6. It is possible for an Irrational number to also be an Integer. ________________________

Short Answer: Read each question carefully and answer it to the best of your ability. Show documentation

of your work when applicable.

7. Give two examples of a terminating decimal and two examples of a repeating decimal, then classify

each number with the name of the appropriate set to which it belongs.

Terminating: 1) Set: ___________________ 2) Set:____________________

Repeating: 1) Set: ___________________ 2) Set:_____________________

8. Give an example of a decimal that is both non-terminating and non-repeating, then classify it by its

most specific set name.

9. Pi is one of the most famous irrational numbers. What characteristics of Pi make it irrational?

10. For fun, and to make a point in the next problem, write down the first 15 digits of Pi (if you can).

11. In your calculator, hit the Pi command, then “enter.” Write down exactly what you see in your

window. What do you notice when comparing these numbers to what we know to be the digits of Pi?Why would this information be important to know?

12. a) What fraction does “1 divided by 3” represent?

b) Enter “1 divided by 3” in your calculator. What answer do you get?

c) Is it safe to assume that 1/3 is rational?




13. a) What fraction does “2 divided by 3” represent?

b) Enter “2 divided by 3” in your calculator. What answer do you get?

c) Is it safe to assume that 2/3 is rational?

14. Is 0.3333 different than 1/3?

12. When writing a decimal number out, how can I show that 0.3333 is different than 1/3?

13. Is 3.14 different than Pi?

14. When writing out the digits of Pi, how can I show that it is Pi, rather than simply the number 3.14?

Quick Skill Practice: Complete the following basic arithmetic problems. Show work when necessary

(especially for fractions).

a. )3(5 b. 118 c. )3(5

d. )7(8 e. )17(2 f. 611

g. 23

21 h.

21

31 i.

83

45

j. 6

1

6

5k.

4

5

4

3l.

3

5

3

1




m. )4(5 n. )3)(7( o. 318

p. 2

1

2

7q.

3

1

8

3r.

7

2

11

5

s.

3

2

3

1t.

3

5

4

1u.

11

3

7

5

1 real number system-1

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